1. Calculus Of Variations - Wikipedia, The Free Encyclopedia Retrieved from http//en.wikipedia.org/wiki/calculus_of_variations . Categories Calculus of variations Fundamental physics concepts Mathematical http://en.wikipedia.org/wiki/Calculus_of_variations

Calculus of variations From Wikipedia, the free encyclopedia Jump to: navigation search Calculus of variations is a field of mathematics that deals with functionals , as opposed to ordinary calculus which deals with functions . Such functionals can for example be formed as integrals involving an unknown function and its derivatives. The interest is in extremal functions: those making the functional attain a maximum or minimum value. Perhaps the simplest example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is obviously a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist. Such solutions are known as geodesics . A related problem is posed by Fermat's principle : light follows the path of shortest optical length connecting two points, where the optical length depends upon the material of the medium. One corresponding concept in mechanics is the principle of least action . The theory of optimal control concerns a specific kind of problem in the calculus of variations.

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Web Shopping Articles Local ... Search Engine Marketing Search for: in: All The Internet Images Google Yahoo Altavista Fast Ask Jeeves Lycos MSN Wisenut Hotbot AOL Search Teoma Home Internet Search Directory Shopping Search Local Search ... Search Engine Marketing Calculus of Variations Home Science Math Calculus Sites in Calculus of Variations Brachistochrone Problem Gives details on how to arrive at the general solutions. Includes definition of terms. http://home.imm.uran.ru/iagsoft/mirr/eric/Brach.html Calculus of Variations and Geometric Measure Theory at Pisa Preprints on various topics on the calculus of variations. http://cvgmt.sns.it/ Calculus of Variations and Optimal Control Calculus of variations and optimal control. Optimization. http://www.math.niu.edu/~rusin/known-math/index/49-XX.html Springer LINK: Calculus of Variations Journal with table of contents and article abstracts back to 1995. Full text available to subscribers only. http://link.springer.de/link/service/journals/00526/

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Home Help Login Logout ... Random Open Dictionary Dedicated to the pursuit of knowledge Advanced Top Mathematics Calculus ... Calculus of Variations Competing Definitions Calculus of Variations [hits=1 votes=1 rating=5.0] : 49: Calculus of variations and optimal control; optimization - Calculus of variations and optimal control; Entry 49 of The Mathematical Atlas on Calculus of variations and optimal control; optimization Calculus of Variations [hits=1 votes=1 rating=5.0] : Calculus of Variations from MathWorld Questions? Bug report? Send email to the Open Dictionary Administrator The Open Dictionary is a World Wide Web of Knowledge (W3K) project.

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Novi upisi Hot Top Nas Izbor ... DIR Search: search the entire directory search this category only Top Science Math Calculus See also: Science: Physics: Classical Mechanics: Lagrangian and Hamiltonian Mechanics Brachistochrone Construction - Here one can see a graph of the brachistochrone for the given endpoint. Java applet. Calculus of Variations and Geometric Measure Theory at Pisa - Preprints on various topics on the calculus of variations. Calculus of Variations and Optimal Control - Calculus of variations and optimal control. Optimization. Calculus of Variations and Partial Differential Equations - Journal with table of contents and article abstracts back to 1995. Full text available to subscribers only. Minimal Surfaces and Isoperimetric Problems - Research group is devoted to variational problems related with the area operator, concerning the minimal surface theory and isoperimetric problems. Includes list of conferences and publications. University of Grenada, Spain. Pocetna Novi upisi Hot Top ... Brzi Oglasi

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Arts Business Computers Games ... ABOUT Options: Directory Entire Web Top Science Math Calculus Calculus of Variations Top/Science/Physics/Classical Mechanics/Lagrangian and Hamiltonian Mechanics Calculus of Variations and Partial Differential Equations - Journal with table of contents and article abstracts back to 1995. Full text available to subscribers only. Minimal Surfaces and Isoperimetric Problems - Research group is devoted to variational problems related with the area operator, concerning the minimal surface theory and isoperimetric problems. Includes list of conferences and publications. University of Grenada, Spain. http://www.ugr.es/local/pvrarea Brachistochrone Construction - Here one can see a graph of the brachistochrone for the given endpoint. Java applet. http://home.ural.ru/~iagsoft/BrachJ2.html Calculus of Variations and Optimal Control - Calculus of variations and optimal control. Optimization. http://www.math.niu.edu/~rusin/known-math/index/49-XX.html Calculus of Variations and Geometric Measure Theory at Pisa - Preprints on various topics on the calculus of variations. http://cvgmt.sns.it/

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Calculus of variations From LoveToKnow 1911 CALCULUS OF VARIATIONS, in mathematics . The calculus of variations arose from the attempts that were made by Origin mathematicians in the 17th century to solve problems of the of which the following are typical examples. (i) It Calculus. is required to determine the form of a chain of given length, hanging from two fixed points, by the condition that its centre of gravity must be as low as possible. This problem of the catenary was attempted without success by Galileo Galilei (1638). (ii) The resistance of a medium to the motion of a body being assumed to be a normal pressure, proportional to the square of the cosine of the angle between the normal to the surface and the direction of motion, it is required to determine the meridian curve of a surface of revolution, about an axis in the direction of motion, so that the resistance shall be the least possible. This problem of the solid of least resistance was solved by Sir Isaac Newton (1687). (iii) It is required to find a curve joining two fixed points, so that the time of descent along this curve from the higher point to the lower may be less than the time along any other curve. This problem of the brachistochrone was proposed by John (Johann) Bernoulli The contributions of the Greek geometry to the subject consist of a few theorems discovered by one Zenodorus, of whom little

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Indopedia Main Page FORUM Help ... Log in The Indology CMS In other languages: Deutsch Categories Mathematical analysis Calculus of variations ... Wikipedia Article Calculus of variations ज्ञानकोश: - The Indological Knowledgebase Calculus of variations is a field of mathematics which deals with functions of functions, as opposed to ordinary calculus which deals with functions of numbers. Such functionals can for example be formed as integrals involving an unknown function and its derivatives. The interest is in extremal functions: those making the functional attain a maximum or minimum value. Some classical problems on curves were posed in this form: one example is the brachistochrone , the path along which a particle would descend under gravity in the shortest time from a given point A to a point B not directly beneath it. Amongst the curves from A to B one has to minimise the expression representing the time of descent. The key theorem of calculus of variations is the Euler-Lagrange equation . This corresponds to the stationary condition on a functional. As in the case of finding the maxima and minima of a function, the analysis of small changes round a supposed solution gives a condition, to first order. It cannot tell one directly whether a maximum or minimum has been found. Variational methods are important in theoretical physics : in Lagrangian mechanics and in application of the principle of stationary action to quantum mechanics . They were also much used in the past in pure mathematics, for example the use of the

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var language=0; var from='english'; var to='english'; Online Dictionary Chinese to English English to Chinese ... French to English German to English to Japanese Italian to English Japanese to English to German Latin to English Russian to English ... Swedish to English If you can't find the translation you need, try our free translation Calculus Of Variations - English Dictionary 1. the calculus of maxima and minima of definite integrals Related words calculus mathematics A B ... Z All content on this website is property of LocalTranslation unless stated otherwise. document.getElementById("generationTime").innerHTML='('+(0.6)+' seconds)'; document.getElementById("generationTime").innerHTML='('+(0.6)+' seconds)';

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Office Supplies Buy Posters A-Z Products Website Advertising ... Calculus of variations Calculus of variations is a field of mathematics which deals with functions of functions, as opposed to ordinary calculus which deals with functions of numbers. Such 'functionals' can for example be formed as integrals involving an unknown function and its derivatives. The interest is in extremal functions: those making the functional attain a maximum or minimum value. Some classical problems on curves were posed in this form: one example is the brachistochrone , the path along which a particle would descend under gravity in the shortest time from a given point A to a point B not directly beneath it. Amongst the curves from A to B one has to minimise the expression representing the time of descent. The key theorem of calculus of variations is the Euler-Lagrange equation[?] . This corresponds to the stationary condition on a functional. As in the case of finding the maxima and minima of a function, the analysis of small changes round a supposed solution gives a condition, to first order. It cannot tell one directly whether a maximum or minimum has been found. Variational methods are important in theoretical physics[?]

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18. Menger On The Calculus Of Variations JOC/EFR March 2006. The URL of this page is http//wwwhistory.mcs.st-andrews. ac.uk/Extras/calculus_of_variations.html. http://www-groups.dcs.st-and.ac.uk/~history/Extras/Calculus_of_Variations.html

Menger on the Calculus of Variations Karl Menger wrote an article What Is Calculus of Variations and What Are Its Applications? This interesting article, written by an outstanding mathematician and expert in the field, gives insights into both the history of the topic and also into understanding Menger's views on mathematics:- The calculus of variations belongs to those parts of mathematics whose details it is difficult to explain to a non-mathematician. It is possible, however, to explain its main problems and to sketch its principal methods for everybody. The first human being to solve a problem of calculus of variations seems to have been Queen Dido of Carthage. When she was promised as much land as might lie within the boundaries of a bull's hide, she cut the hide into many thin strips, put them together into one long strip, the ends of which she united, and then she tried to secure as extensive a territory as possible within this boundary. History does not describe the form of the territory she chose, but if she was a good mathematician she covered the territory in the form of a circle, for today we know: Of all surfaces bounded by curves of a given length, the circle is the one of largest area. The branch of mathematics which establishes a rigorous proof of this statement is the calculus of variations. Newton was the first mathematician to publish a result in this field. If a body moves in the air, it meets with a certain resistance, which depends on the shape of the body. The problem Newton studied was, what shape of body would guarantee the least possible resistance? Applications of this problem are obvious. The rifle bullet is designed in such shape as to meet with a minimum resistance in the air. Newton published a correct answer to a special case of this problem, namely, that the surface of the solid considered is obtained by revolving a curve around an axis. But he did not give the proof or the calculations that had led him to the answer. So Newton's solution had no great effect on the development of mathematics.

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